scholarly journals Exponential Feedback Passivity of Switched Polynomial Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Huawei Zhu ◽  
Xiaorong Hou
Keyword(s):  
Nonlinear Systems ◽  
External Disturbance ◽  
Robust Stabilization ◽  
Solution Algorithm ◽  
Switched Nonlinear Systems ◽  
Parameter Uncertainties ◽  
Numerical Example

The exponential feedback passivity problem of switched polynomial nonlinear systems is studied. To obtain this aim, a method of parameterization of controller is presented and parameter solution algorithm is described. Then, the addressed method is utilized to solve the robust stabilization for a class of switched polynomial nonlinear systems with parameter uncertainties and external disturbance. This result extends the previous results on exponential feedback passivity from the case of nonlinear systems to switched nonlinear systems. A numerical example is given to demonstrate the effectiveness of the proposed result.

scholarly journals A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Cao ◽  
Xiaorong Hou
Keyword(s):  
Nonlinear Systems ◽  
Hamiltonian Systems ◽  
Symbolic Computation ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Internal Stability ◽  
Parameterization Method ◽  
Numerical Example ◽  
Isaacs Equations ◽  
Controller Parameterization

This paper considers controller parameterization method ofH∞control for polynomial Hamiltonian systems (PHSs), which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems areH∞stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimizeH∞control by adjusting parameters. All these results are expected to be of use in the study ofH∞control for nonlinear systems with perturbations.

ROBUST AUTONOMOUS HELICOPTER STABILIZER TUNED BY PARTICLE SWARM OPTIMIZATION

2014 ◽  
Vol 28 (01) ◽  
pp. 1459002 ◽  
Author(s):  
KUMERESAN A. DANAPALASINGAM
Keyword(s):  
Particle Swarm Optimization ◽  
External Disturbance ◽  
Robust Stabilization ◽  
Particle Swarm ◽  
Wind Disturbance ◽  
Parameter Uncertainties ◽  
Swarm Optimization ◽  
A Chain ◽  
Tuning Methods ◽  
Autonomous Helicopter

Autonomous helicopter stabilization in the presence of a wind disturbance is presented. A controller is designed based on the nonlinear adaptive output regulation and robust stabilization of a chain of integrators by a saturated feedback to stabilize the position and velocity of a helicopter. The controller is able to adaptively estimate the wind disturbance whose measurements are not made available. In addition to robustness against the external disturbance input the control design is carried out to handle helicopter parameter uncertainties. The cost of the robustly stabilizing control strategy is the challenge to tune 13 controller parameters for a desired output response. Particle swarm optimization (PSO), a metaheuristic optimization algorithm is applied to automate the tuning process. Simulation results demonstrate the effectiveness of the proposed control and tuning methods in the robust stabilization of the helicopter motion.

scholarly journals H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control

2010 ◽  
Vol 5 (4) ◽  
pp. 592 ◽  
Author(s):  
Xizheng Zhang ◽  
Yaonan Wang ◽  
Xiaofang Yuan
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Mode Control ◽  
Disturbance Attenuation Level ◽  
Takagi Sugeno

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with state delay, which can be represented by a Takagi-Sugeno (TS) model with uncertainties. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H∞ technique such that the robust asymptotically stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified switching surface is proven. Simulation results show the validity of the proposed method.

Robust Stabilization for a Class of Switched Nonlinear Systems

2012 ◽  
Vol 490-495 ◽  
pp. 1536-1540
Author(s):  
Cai Yun Wu ◽  
Ben Niu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
Closed Loop System ◽  
Multiple Lyapunov Functions ◽  
Switching Law ◽  
Nonlinear Part ◽  
State Dependent

This paper addresses the stabilization problem for a class of switched nonlinear systems with Lipschitz nonlinearities using the multiple Lyapunov functions (MLFs) approach. A state feedback controller and a state dependent switching law are proposed to asymptotic stabilization the switched system via linear matrix inequalities (LMI). The developed control strategy ensures asymptotic stability of the closed-loop system even if the nonlinear part . Finally, the feasibility of the proposed method is illustrated through a simulation example

scholarly journals On Finite-Time Stability of Switched Systems with Hybrid Homogeneous Degrees

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bin Zhang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Nonlinear Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Numerical Example

The finite-time stability is investigated for switched nonlinear systems. It is assumed that each subsystem possesses a positive homogeneous Lyapunov-like function. The derivative of the function is with hybrid homogenous degrees. Three substantially different situations are considered and different sufficient conditions are provided, respectively. The utility of our result is illustrated through the study of a numerical example.

scholarly journals Robust Reliable Stabilization of Switched Nonlinear Systems with Time-Varying Delays and Delayed Switching

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Zhengrong Xiang ◽  
Qingwei Chen
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Actuator Failure ◽  
Exponentially Stable

This paper is concerned with the problem of robust reliable stabilization of switched nonlinear systems with time-varying delays and delayed switching is investigated. The parameter uncertainties are allowed to be norm-bounded. The switching instants of the controller experience delays with respect to those of the system. The purpose of this problem is to design a reliable state feedback controller such that, for all admissible parameter uncertainties and actuator failure, the system state of the closed-loop system is exponentially stable. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of linear matrix inequalities (LMIs).

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